I have emailed them with this specific question almost a year ago and got this response:
Throughout development Neuromod has taken steps to ensure that the relationship between the sound and tongue stimulus is well defined and reliable. These steps involved characterising the delay of the Bluetooth link to the provided headphones (AKG K845BT headphones) and compensating for this delay during treatment sessions. Neuromod has performed extensive validation to ensure that the required timing relationship is consistent and repeatable. This is currently one of the reasons why the Lenire® device restricts operation to just the AKG headphones – use with other Bluetooth devices is currently not possible.
I'm not tech-savvy enough to know if it is indeed possible for the compensation of this delay to be "consistent and repeatable", but it sounds like they've put thought into it.